Find the Domain and Range y=4+ square root of x+6

$y = 4 + \sqrt{x + 6}$

Step 1

Set the radicand in $\sqrt{x + 6}$ greater than or equal to $0$ to find where the expression is defined.

$x + 6 \geq 0$

Step 2

Subtract $6$ from both sides of the inequality.

$x \geq - 6$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[- 6, \infty)$

Set-Builder Notation:

${x | x \geq - 6}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$[4, \infty)$

Set-Builder Notation:

${y | y \geq 4}$

Step 5

Determine the domain and range.

Domain: $[- 6, \infty), {x | x \geq - 6}$

Range: $[4, \infty), {y | y \geq 4}$

Step 6